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Solutions to Net Present Value and Other Investment Criteria document sample
Chapter 9 Net Present Value and Other Investment Criteria -- THE BASICS OF CAPITAL BUDGETING Should we build this plant? BMGT440 – Dr. E F Kiss -1 Key Concepts and Skills Be able to compute payback and discounted payback and understand their shortcomings Understand accounting rates of return and their shortcomings Be able to compute the internal rate of return and understand its strengths and weaknesses Be able to compute the net present value and understand why it is the best decision criterion BMGT440 – Dr. E F Kiss -2 Chapter Outline Net Present Value The Payback Rule The Discounted Payback The Average Accounting Return The Internal Rate of Return The Profitability Index Modified Rate of Return The Practice of Capital Budgeting BMGT440 – Dr. E F Kiss -3 WHAT IS CAPITAL BUDGETING? Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future. conceptually, capital budget process is identical to decision process used by individuals making investment decisions BMGT440 – Dr. E F Kiss -4 Steps: 1. Estimate CFs (inflows & outflows). 2. Assess riskiness of CFs (Cash Flows). 3. Determine R = WACC (adj.). determine appropriate discount rate, based on riskiness of Cash Flows & general level int.rates 4. Find NPV of the expected cash flows and/or IRR. 5. Accept if NPV > 0 and/or IRR > WACC. BMGT440 – Dr. E F Kiss -5 An Example of Mutually Exclusive Projects: BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other. projects are independent if CF of 1 not affected by acceptance of other BMGT440 – Dr. E F Kiss -6 Good Decision Criteria We need to ask ourselves the following questions when evaluating decision criteria § Does the decision rule adjust for the time value of money? § Does the decision rule adjust for risk? § Does the decision rule provide information on whether we are creating value for the firm? BMGT440 – Dr. E F Kiss -7 Project Example Information You are looking at a new project and you have estimated the following cash flows: § Year 0: CF = -165,000 § Year 1: CF = 63,120; NI = 13,620 § Year 2: CF = 70,800; NI = 3,300 § Year 3: CF = 91,080; NI = 29,100 § Average Book Value = 72,000 Your required return for assets of this risk is 12%. BMGT440 – Dr. E F Kiss -8 Net Present Value The difference between the market value of a project and its cost How much value is created from undertaking an investment? § The first step is to estimate the expected future cash flows. § The second step is to estimate the required return for projects of this risk level. § The third step is to find the present value of the cash flows and subtract the initial investment. BMGT440 – Dr. E F Kiss -9 NPV – Decision Rule If the NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. n CFt NPV t 0 1 R t . n CFt NPV CF0 . t 1 1 R t BMGT440 – Dr. E F Kiss -10 Computing NPV for the Project Using the formulas: § NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = 12,627.42 Using the calculator: § CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.42 Do we accept or reject the project? BMGT440 – Dr. E F Kiss -11 Decision Criteria Test - NPV Does the NPV rule account for the time value of money? Does the NPV rule account for the risk of the cash flows? Does the NPV rule provide an indication about the increase in value? Should we consider the NPV rule for our primary decision criteria? BMGT440 – Dr. E F Kiss -12 Calculating NPVs with a Spreadsheet Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. Using the NPV function § The first component is the required return entered as a decimal § The second component is the range of cash flows beginning with year 1 § Subtract the initial investment after computing the NPV BMGT440 – Dr. E F Kiss -13 Payback Period How long does it take to get the initial cost back in a nominal sense? Computation § Estimate the cash flows § Subtract the future cash flows from the initial cost until the initial investment has been recovered Decision Rule – Accept if the payback period is less than some preset limit BMGT440 – Dr. E F Kiss -14 Computing Payback For The Project Assume we will accept the project if it pays back within two years. § Year 1: 165,000 – 63,120 = 101,880 still to recover § Year 2: 101,880 – 70,800 = 31,080 still to recover § Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3 Do we accept or reject the project? BMGT440 – Dr. E F Kiss -15 Decision Criteria Test - Payback Does the payback rule account for the time value of money? Does the payback rule account for the risk of the cash flows? Does the payback rule provide an indication about the increase in value? Should we consider the payback rule for our primary decision criteria? BMGT440 – Dr. E F Kiss -16 Advantages and Disadvantages of Payback Advantages Disadvantages § Easy to understand § Ignores the time § Adjusts for value of money uncertainty of later § Requires an arbitrary cash flows cutoff point § Biased towards § Ignores cash flows liquidity beyond the cutoff date § Biased against long- term projects, such as research and development, and new projects BMGT440 – Dr. E F Kiss -17 Discounted Payback Period Compute the present value of each cash flow and then determine how long it takes to payback on a discounted basis Compare to a specified required period Decision Rule - Accept the project if it pays back on a discounted basis within the specified time BMGT440 – Dr. E F Kiss -18 Computing Discounted Payback for the Project Assume we will accept the project if it pays back on a discounted basis in 2 years. Compute the PV for each cash flow and determine the payback period using discounted cash flows § Year 1: 165,000 – 63,120/1.121 § 165,000 – 56,357.14 = 108,643 § Year 2: 108,643 – 70,800/1.122 § 108,643 – 56,441.33 = 52,202 § Year 3: 52,202 – 91,080/1.123 § 52,202 – 64,828.94 = -12,627 project pays back in year 3 Do we accept or reject the project? BMGT440 – Dr. E F Kiss -19 Decision Criteria Test – Discounted Payback Does the discounted payback rule account for the time value of money? Does the discounted payback rule account for the risk of the cash flows? Does the discounted payback rule provide an indication about the increase in value? Should we consider the discounted payback rule for our primary decision criteria? BMGT440 – Dr. E F Kiss -20 Advantages and Disadvantages of Discounted Payback Advantages Disadvantages § Includes time value § May reject positive of money NPV investments § Easy to understand § Requires an arbitrary § Does not accept cutoff point negative estimated § Ignores cash flows NPV investments beyond the cutoff § Biased towards point liquidity § Biased against long- term projects, such as R&D and new products BMGT440 – Dr. E F Kiss -21 Average Accounting Return There are many different definitions for average accounting return The one used in the book is: § Average net income / average book value § Note that the average book value depends on how the asset is depreciated. Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate. BMGT440 – Dr. E F Kiss -22 Computing AAR For The Project Assume we require an average accounting return of 25% Average Net Income: § (13,620 + 3,300 + 29,100) / 3 = 15,340 AAR = 15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project? BMGT440 – Dr. E F Kiss -23 Decision Criteria Test - AAR Does the AAR rule account for the time value of money? Does the AAR rule account for the risk of the cash flows? Does the AAR rule provide an indication about the increase in value? Should we consider the AAR rule for our primary decision criteria? BMGT440 – Dr. E F Kiss -24 Advantages and Disadvantages of AAR Advantages Disadvantages § Easy to calculate § Not a true rate of § Needed information return; time value of will usually be money is ignored available § Uses an arbitrary benchmark cutoff rate § Based on accounting net income and book values, not cash flows and market values BMGT440 – Dr. E F Kiss -25 Internal Rate of Return This is the most important alternative to NPV It is often used in practice and is intuitively appealing It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere BMGT440 – Dr. E F Kiss -26 IRR – Definition and Decision Rule Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return NPV: Enter R, solve for NPV. n CFt 1 R t NPV . t 0 IRR: Enter NPV = 0, solve for IRR. n CFt t 0 1 IRR t 0. BMGT440 – Dr. E F Kiss -27 Computing IRR For The Project If you do not have a financial calculator, then this becomes a trial and error process Calculator § Enter the cash flows as you did with NPV § Press IRR and then CPT § IRR = 16.13% > 12% required return Do we accept or reject the project? BMGT440 – Dr. E F Kiss -28 NPV Profile For The Project 70,000 60,000 IRR = 16.13% 50,000 40,000 30,000 NPV 20,000 10,000 0 -10,000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 -20,000 Discount Rate BMGT440 – Dr. E F Kiss -29 Decision Criteria Test - IRR Does the IRR rule account for the time value of money? Does the IRR rule account for the risk of the cash flows? Does the IRR rule provide an indication about the increase in value? Should we consider the IRR rule for our primary decision criteria? BMGT440 – Dr. E F Kiss -30 Advantages of IRR Knowing a return is intuitively appealing It is a simple way to communicate the value of a project to someone who does not know all the estimation details If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task BMGT440 – Dr. E F Kiss -31 Summary of Decisions For The Project Summary Net Present Value Accept Payback Period Reject Discounted Payback Period Reject Average Accounting Return Reject Internal Rate of Return Accept BMGT440 – Dr. E F Kiss -32 Calculating IRRs With A Spreadsheet You start with the cash flows the same as you did for the NPV You use the IRR function § You first enter your range of cash flows, beginning with the initial cash flow § You can enter a guess, but it is not necessary § The default format is a whole percent – you will normally want to increase the decimal places to at least two BMGT440 – Dr. E F Kiss -33 NPV Vs. IRR NPV and IRR will generally give us the same decision Exceptions § Non-conventional cash flows – cash flow signs change more than once § Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different BMGT440 – Dr. E F Kiss -34 IRR and Non-conventional Cash Flows When the cash flows change sign more than once, there is more than one IRR When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation If you have more than one IRR, which one do you use to make your decision? BMGT440 – Dr. E F Kiss -35 Another Example – Non-conventional Cash Flows Suppose an investment will cost $90,000 initially and will generate the following cash flows: § Year 1: 132,000 § Year 2: 100,000 § Year 3: -150,000 The required return is 15%. Should we accept or reject the project? BMGT440 – Dr. E F Kiss -36 NPV Profile IRR = 10.11% and 42.66% $4,000.00 $2,000.00 $0.00 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ($2,000.00) NPV ($4,000.00) ($6,000.00) ($8,000.00) ($10,000.00) Discount Rate BMGT440 – Dr. E F Kiss -37 Summary of Decision Rules The NPV is positive at a required return of 15%, so you should Accept If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject You need to recognize that there are non- conventional cash flows and look at the NPV profile BMGT440 – Dr. E F Kiss -38 IRR and Mutually Exclusive Projects Mutually exclusive projects § If you choose one, you can’t choose the other § Example: You can choose to attend graduate school next year at either Harvard or Stanford, but not both Intuitively you would use the following decision rules: § NPV – choose the project with the higher NPV § IRR – choose the project with the higher IRR BMGT440 – Dr. E F Kiss -39 Example With Mutually Exclusive Projects Period Project A Project The required return B for both projects is 10%. 0 -500 -400 1 325 325 Which project 2 325 200 should you accept and why? IRR 19.43% 22.17% NPV 64.05 60.74 BMGT440 – Dr. E F Kiss -40 NPV Profiles $160.00 IRR for A = 19.43% $140.00 $120.00 IRR for B = 22.17% $100.00 Crossover Point = 11.8% $80.00 NPV A $60.00 B $40.00 $20.00 $0.00 ($20.00) 0 0.05 0.1 0.15 0.2 0.25 0.3 ($40.00) Discount Rate BMGT440 – Dr. E F Kiss -41 Conflicts Between NPV and IRR NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another decision rule, you should always use NPV IRR is unreliable in the following situations § Non-conventional cash flows § Mutually exclusive projects BMGT440 – Dr. E F Kiss -42 Profitability Index Measures the benefit per unit cost, based on the time value of money A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value This measure can be very useful in situations where we have limited capital BMGT440 – Dr. E F Kiss -43 Advantages and Disadvantages of Profitability Index Advantages Disadvantages § Closely related to § May lead to incorrect NPV, generally decisions in leading to identical comparisons of decisions mutually exclusive § Easy to understand investments and communicate § May be useful when available investment funds are limited BMGT440 – Dr. E F Kiss -44 More examples What is the payback period? The expected number of years required to recover a project’s cost, or how long does it take to get our money back? calculate payback by developing the cumulative CF as shown on next slide for project L Our examples use projects L (long) and S (short) BMGT440 – Dr. E F Kiss -45 Payback for Project L (Long: Most CFs in out years) 0 1 2 2.4 3 CFt -100 10 60 80 . Cumulative -100 -90 -30 0 50 PaybackL = 2 + 30/80 = 2.375 years BMGT440 – Dr. E F Kiss -46 Project S (Short: CFs come quickly) 0 1 1.6 2 3 -100 70 . 50 20 CFt Cumulative -100 -30 0 20 40 PaybackL = 1 + 30/50 = 1.6 years BMGT440 – Dr. E F Kiss -47 C. 3. Discounted Payback: Uses discounted rather than raw CFs. 0 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumulative -100 -90.91 -41.32 18.79 Disc. = 2 + 41.32/60.11 = 2.687 yrs payback Recover investment + cap costs in 2.7 yrs. BMGT440 – Dr. E F Kiss -48 NPV: Sum of the PVs of inflows and outflows. n CFt NPV . t 0 R t 1 Cost often is CF0 and is negative. n CFt NPV CF0 . t 1 R t 1 BMGT440 – Dr. E F Kiss -49 What’s Project L’s NPV? Project L: 0 1 2 3 10% -100.00 10 60 80 9.09 49.59 60.11 $18.79 = NPVL NPVS = $19.98. BMGT440 – Dr. E F Kiss -50 Calculator Solution: Enter in CFLO for L: -100 CF0 10 CF1 60 CF2 80 CF3 10 I NPV = $18.78 = NPVL BMGT440 – Dr. E F Kiss -51 Rationale for the NPV Method NPV = PV inflows - Cost = Net gain in wealth. For independent projects, Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Choose the one that adds the most value. BMGT440 – Dr. E F Kiss -52 Using NPV method, which project(s) should be accepted? If Projects S and L are mutually exclusive, accept S because NPVs > NPVL . If S & L are independent, accept both; NPV > 0. BMGT440 – Dr. E F Kiss -53 Would the NPVs change if the cost of capital changed? The NPV of a project is dependent on the cost of capital used. if the cost of capital changed, the NPV of each project would change. NPV declines as R increases and NPV rises as R falls BMGT440 – Dr. E F Kiss -54 Internal Rate of Return: IRR 0 1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0. BMGT440 – Dr. E F Kiss -55 NPV: Enter R, solve for NPV. n CFt 1 R t NPV . t 0 IRR: Enter NPV = 0, solve for IRR. n CFt 1 IRR t 0. t 0 BMGT440 – Dr. E F Kiss -56 What’s Project L’s IRR? 0 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3 0 = NPV Enter CFs in CFLO, then press, IRR: IRRL = 18.13%. IRRS = 23.56%. BMGT440 – Dr. E F Kiss -57 Find IRR if Cash Flows are constant: 0 1 2 3 IRR = ? -100 40 40 40 INPUTS 3 -100 40 0 N I/YR PV PMT FV OUTPUT OUTPUT 9.70% Or, with CFLO, enter CFs and press IRR = 9.70%. BMGT440 – Dr. E F Kiss -58 How is a project’s IRR related to a bond’s YTM? They are the same thing. A bond’s YTM is the IRR if you invest in the bond. 0 1 2 10 IRR = ? -1134.2 90 90 1090 IRR = 7.08% (use TVM or CFLO). BMGT440 – Dr. E F Kiss -59 . Rationale for the IRR method: If IRR > WACC, then the project’s rate of return is greater than its cost => some return is left over to boost stockholders’ returns. Example: WACC = 10%, IRR = 15%. Profitable. BMGT440 – Dr. E F Kiss -60 IRR acceptance criteria: If IRR > R, accept project. If IRR < R, reject project. BMGT440 – Dr. E F Kiss -61 Decisions on our Projects S and L per IRR: If S and L are independent, accept both. IRRs > R = 10%. If S and L are mutually exclusive, accept S because IRRS > IRRL . BMGT440 – Dr. E F Kiss -62 would the projects’ IRRs change if the cost of capital changed? IRRs are independent of the cost of capital therefore, neither IRR s nor IRR L would change if R changed however, the acceptability of the projects could change § L would be rejected if R were above 18.1% § S would also be rejected if R were > 23.6% BMGT440 – Dr. E F Kiss -63 Reinvestment Rate Assumptions NPV assumes reinvest at R (opportunity cost of capital). IRR assumes reinvest at IRR. Reinvest at opportunity cost, R, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. BMGT440 – Dr. E F Kiss -64 Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash inflows are reinvested at WACC. BMGT440 – Dr. E F Kiss -65 MIRR for Project L (R = 10%): 0 1 2 3 10% -100.0 10.0 60.0 80.0 10% 66.0 PV outflows 10% 12.1 MIRR = 158.1 -100.0 16.5% TV inflows $100 = $158.1 (1+MIRRL)3 = 16.5%; MIRRL – Dr. E F Kiss BMGT440 in table A-3: 1.581 = 158.1/100 LookFin 103 - Chapter 10 - Dr. Elinda Fishman Kiss= PMT; find R when N=3 -66 To find TV with HP10B, enter in CFLO: CF0 = 0, CF1 = 10 , CF2 = 60, CF3 = 80 i = 10 NPV = 118.78 = PV of inflows. EnterPV = -188.78, N = 3, i = 10, PMT = 0. Press FV = 158.10 = FV of inflows. Enter FV = 158.10, PV = -100, PMT = 0, N = 3. Press i = 16.50% = MIRR. BMGT440 – Dr. E F Kiss -67 Why use MIRR versus IRR? MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR. BMGT440 – Dr. E F Kiss -68 Define Profitability Index n CIFt 1 R t t 0 PI n . COFt 1 R t t 0 BMGT440 – Dr. E F Kiss -69 What is each franchise’s PI? $9.09 $49.59 $60.11 PI L $100 1.1879 1.19. PIS ($63.636 $41.32 $15.03) / $100 1.1998 1.20. Accept project if PI > 1.0. BMGT440 – Dr. E F Kiss -70 Capital Budgeting In Practice We should consider several investment criteria when making decisions NPV and IRR are the most commonly used primary investment criteria Payback is a commonly used secondary investment criteria BMGT440 – Dr. E F Kiss -71 Summary – Discounted Cash Flow Criteria Net present value § Difference between market value and cost § Take the project if the NPV is positive § Has no serious problems § Preferred decision criterion Internal rate of return § Discount rate that makes NPV = 0 § Take the project if the IRR is greater than required return § Same decision as NPV with conventional cash flows § IRR is unreliable with non-conventional cash flows or mutually exclusive projects Profitability Index § Benefit-cost ratio § Take investment if PI > 1 § Cannot be used to rank mutually exclusive projects § May be use to rank projects in the presence of capital BMGT440 – rationing Dr. E F Kiss -72 Summary – Payback Criteria Payback period § Length of time until initial investment is recovered § Take the project if it pays back in some specified period § Doesn’t account for time value of money and there is an arbitrary cutoff period Discounted payback period § Length of time until initial investment is recovered on a discounted basis § Take the project if it pays back in some specified period § There is an arbitrary cutoff period BMGT440 – Dr. E F Kiss -73 Summary – Accounting Criterion Average Accounting Return § Measure of accounting profit relative to book value § Similar to return on assets measure § Take the investment if the AAR exceeds some specified return level § Serious problems and should not be used BMGT440 – Dr. E F Kiss -74 Quick Quiz Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. § What is the payback period? § What is the discounted payback period? § What is the NPV? § What is the IRR? § What is the MIRR? § What is the PI? § Should we accept the project? What decision rule should be the primary decision method? When is BMGT440 – Dr. E F Kiss the IRR rule unreliable? -75